Course Announcements
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4/27/21
1. Anonymous grades for Final Exam and the semester have been posted.
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4/26/21
1. Anonymous grades for Exam 2 posted.
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4/16/21
1. The time of the alternate session for the Final Exam has been
posted on the exam information page.
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4/13/21
1. Solutions to Exam 2 have been posted.
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4/12/21
1. Solutions to Study Question Homework 5 on nonlinear equations have been posted.
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4/7/21
1. Study Question Homework 5 on nonlinear equations has been posted. Solutions will be posted this weekend.
2. There will be no more graded homework. You are encouraged to use the
study questions just posted and experiments on code to verify examples and probe the behavior of the methods for nonlinear equations that have been and will be discussed.
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4/6/21
1. Sets 14 and 15 of the class notes have been posted.
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4/5/21
1. Final Exam information has been posted.
2. Anonymous Grades for Exam 1 have been posted and canvas
has your marked up exams and grade summary.
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4/2/21
1. Those that plan to take Exam 2 in the alternate session
Thursday morning should send email to me immediately.
2. Anonymous grade list for Exam 1 has been posted.
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4/2/21
1. In Graded Homework 4 the list of codes has the phrase
"with a stationary mode option" was used in the precondtioned SD code bullet. This was not discussed in class or material that you are responsible so it has been removed and the assignment reposted.
(It means a verison of the code that can run with a fixed stepsize α rather than the SD stepsize αk.)
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4/1/21
1. The clarifications in response to the question in class Wednesday have been added to Set 11 of the class notes.
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3/31/21
1. Class on Friday 4/2/21 will have a face-to-face session in MCH 220.
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3/29/21
1. Set 13 of the class notes has been posted.
2. Exam 2 information has been posted.
3. A review session on zoom is planned for Thursday April 1, 2021
5:30PM to 7:30PM. Requests for additional or alternate times should be made immediately.
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3/25/21
1. Class on Friday 3/26/21 will have a face-to-face session in MCH 220.
2. Two extra sets of slides on stationary methods for linear systems have been posted along with some associated study questions and their solutions. This material is for the FCM qualifier. You are not responsible for it this semester.
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3/24/21
1. Slide 36 of Set 8 of the class notes has been modified a bit
to more clearly reflect the order of use of the properties of CD and
CG to derive the efficient form of CG.
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3/22/21
1. Graded Homework 4 has been posted.
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3/21/21
1. The proof of linear convergence of the Regula Falsi method
at the end of Set 11 has been modified for clarity.
2. Comments on the Cholesky and LU factorizations have been
added to the Comments on Graded Homework 3 document.
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3/20/21
1. Sets 10, 11, and 12 of the class notes has been posted.
It is strongly recommended that you read ahead in these sets.
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3/18/21
1. Class on Friday 3/19/21 will have a face-to-face session in MCH 220.
2. Study Homework Questions 4 and their solutions have been posted.
3. The symbol used for the subspaces spanned by the A-orthogonal vectors pj has been changed to ℬk-1 in Set 8 to avoid confusion with the
symbol, 𝒮k-1, used for the linear variety that is a shifted version of the subspace.
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3/17/21
1. Set 9 of the class notes has been posted.
2. A paper by Sameh et al. has been posted. It is for your reference
and you are not responsible for it this semester. It discuss a class of methods that are related to CG and projection methods. They are related to many algorithms developed for least squares problems in deterministic and random settings, e.g., adaptive filtering in digital signal processing.
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3/15/21
1. Set 8 of the class notes has been posted.
2. Anonymous grades posted for Graded Homeworks 1 and 2
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3/11/21
1. Reminder: Friday will be a face-to-face lecture in MCH 220.
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3/10/21
1. A typo in the solution of Problem 2(a) of Exam 1 has been corrected.
The correct value for the norm is ∥ Fn ∥ = √n
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3/9/21
1. Solutions for Exam 1 have been posted. There was a typo on the DFT questions
that has been fixed the solutions. Your solutions will be graded taking into account
the typo in the statement of the problem.
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3/3/21
1. Study Homework Questions 3 and their solutions have been posted.
2. Zoom meetings have been added for the Alternate Exam 1 time (8:30AM March 4) and the regular Exam 1 time (6:30PM March 4)
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3/4/21
1. Friday 3/5/21 class will have a face-to-face
session in MCH 220.
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3/2/21
1. Set 7 of the class notes has been posted.
2. In Graded Homework 3 in Task 1 on structured matrices
the sentence "Consider factoring with no pivoting, partial pivoting and complete pivoting." Appeared in some cases without the
phrase "and complete pivoting" part due a systematic text processing error. The phrase has been added and the assignment reposted.
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2/27/21
1. Graded Homework 3 (programming of LU only -- no written problems) has been posted. You are strongly encouraged to look a the first set of empirical tasks before the exam. You need not, of course, finish those tasks before the exam but considering them perhaps with the use of a library LU such as MATLAB is encouraged.
2. Set 6 on the stability and conditioning of LU and QR
factorizations and their use in solving systems and least squares problems have been posted. We will concentrate on the conditioning of both problems and the stability of LU. The stability of QR via Householder reflectors will be summarized.
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2/25/21
1. The solutions to Graded Homework 2 have been posted with both the written problems and the programming problem included.
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2/24/21
1. The solutions to the written problems of Graded Homework 2 have been posted.
2. Friday's class will include a face-to-face session in MCH 220 .
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2/23/21
1. Since Monday's review was highly concentrated on a small number of topics, I have added an additional review on Friday 2/26 3:30 PM - 5:30 PM. The next review will be as previsously announced on Thursday 2/25 3:30 PM - 5:30 PM.
2. The alternate time for Exam 1 has been posted on the exam information page.
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2/22/21
1. A typo relevant in the solution of study question 2.1 has been fixed and the pdf file reposted.
1. Exam 1 will be moved to the new date.
2. New slides 79 and 80 on representing elementary and general permutations have been added to Set 4.
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2/18/21
1. The typo (??) has been fixed in the Graded Homework 2 file and it has
been reposted.
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2/18/21
1. In Set 4, slide 69 has been modified and a new slide 70 added.
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2/17/21
1. The face-to-face section will meet during class on this Friday
2/19/21. The classroom is MCH 220.
2. The typo on slide 63 of Set 4 fixed and slides 66 and 69 modified slightly.
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2/16/21
1. The coverage of Exam 1 has been added to the exam information
page
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2/12/21
1. Graded Homework 2 has been posted. It includes
a programming assignment on the DFT/FFT and written problems.
2. Exam 1 information has been posted.
3. Typos on slide 38 of Set 4 fixed. A clarification added on slide 41
and a new slide 43 inserted.
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2/8/21
1. Four additional papers on calculating the bit reversal permutation
have been posted.
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2/2/21
1. Set 5 of the class notes has been posted. It is strongly recommended that you read ahead in preparation for the lectures on this set.
2. Sets 4 and 5 will make up the material for most of February.
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2/1/21
1. Set 4 of the class notes has been posted. It is strongly recommended that you read ahead in preparation for the lectures on this set.
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1/29/21
1. Set 3 of the class notes has been posted.
2. Study Questions Homework 2 and its solutions have been posted.
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1/26/21
1. Sets 1 and 2 of the class notes have been posted.
2. A paper by Gannon and Jalby on parallelization/memory hierarchy issues of FFTs has been posted.
3. A paper on the computation of the bit reversal permutation has been posted. It is also discussed in the FFT textbook of Van Loan.
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1/22/21
1. (Typos fixed) A set of comments on 2 x 2 matrix eigenvalues useful for the graded homework 1 has been posted.
2. Set 1 of the class notes has been posted.
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1/18/21
1. Graded Homework 1 has been posted.
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1/15/21
1. Slides 10 and 11 of Set 31 from FCM 1 Fall 2020 have been modified slightly and reposted on the FCM 1 webpage. (This includes the typos discussed at the end of class today.)
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1/13/21
1. Solutions for Study Questions Homework 1 have been posted.
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1/5/21
1. The class syllabus has been posted.
2. A description of the format for submitting program solutions has been posted.
3. Example program solutions have been posted.
4. Homework 1 consisting of review problems has been posted.
5. We will be using the Runge Kutta ODE slides of FCM 1 Fall 2020
for the first few classes as mentioned last semester.
6. Set 0 of the class notes has been posted.
7. Review Set 0 to assess how much finite dimensional vector
space theory you have retained. It is also assumed that you know the basics
of solving a linear system in some manner but not necessarily the rigorous
analysis and algorithmic design that will be covered in substantial
detail in this semester.